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Updated: May 6, 2025
And hence it is that in disputes and reasonings concerning eternity, or any other infinite, we are very apt to blunder, and involve ourselves in manifest absurdities. Infinite Divisibility of Matter.
Not only its color, but its tenacity, resistance to decay, and wonderful divisibility, make this bark one of the most remarkable of nature's fabrics. To the Indian and the trapper it has long been as indispensable as is the palm to the native of the tropics.
No restriction was imposed by law on the free divisibility of property.
Instead of this unintelligible jargon, he ought to have contemplated it as a genus of beings, of which the individuals, although they might possess some common properties, such as extent, divisibility, figure, &c. should not, however, be all ranked in the same class, nor comprised under the same general denomination.
This only means that the visual or tactual point of the single experience may stand for, may represent, what is not a mere point but has parts, and is, hence, divisible. Who can set a limit to such possible substitutions? in other words, who can set a limit to the divisibility of a real line? It is only when we confuse the single experience with the real line that we fall into absurdities.
If no one paid for stockings, they would cease to be made; and, with the scarcity, the price would not fail to reappear. The sophism which I am now combating has its root in the infinite divisibility which belongs to value, as it does to matter.
Thus, not having any perfect idea of the LEAST EXTENSION OF MATTER, nor of INFINITY, we are at a loss about the divisibility of matter; but having perfect, clear, and distinct ideas of NUMBER, our reason meets with none of those inextricable difficulties in numbers, nor finds itself involved in any contradictions about them.
I doubt not but, it will readily be allowed by the most obstinate defender of the doctrine of infinite divisibility, that these arguments are difficulties, and that it is impossible to give any answer to them which will be perfectly clear and satisfactory.
Thought is different from motion, perception from impact: the individuality of a mind is hardly consistent with the divisibility of an extended substance; or its volition, that is, its power of originating motion, with the inertness which cleaves to every portion of matter which our observation or our experiments can reach.
When we move a hand or foot, where and how does the action begin? What is the theoretical limit of divisibility or expansion? These and scores of similar questions have only to be asked for us to feel the utter helplessness of our powers of understanding.
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